6.2: Properties of Parallelograms

Objectives:•To use relationships among sides and among angles of parallelograms•To use relationships involving diagonals of parallelograms or transversals

Please note…

• Every property that you learn in this section also applies to rectangles, rhombuses and squares!!!!! They are part of the Parallelogram Family!

• The converse of every theorem in this section is also true.

THEOREM:

Opposite sides of a parallelogram ( ) are congruent.

Example: Given EFGH

Find GH and EG

E F

G H

7

6

Theorem:

Opposite angles of a are congruent.

W V

UT

UW

VT

EXAMPLEC J

G H

115

65

FIND measure of angle J and angle H.

Consecutive Angles

Angles that share a side

D C

BA CDand

BCand

DAand

BAand

In a parallelogram, consecutive angles are supplementary (Because they are same-side interior angles!!)

A B

CD

180

180

180

180

DmCm

BmCm

DmAm

BmAm

Find the values of the variables.

b+7

18

2cc+4

(3a)°60°

Theorem:

The diagonals of a bisect each other. E F

GH

K

KFHK

KGEK

Example: If EK = 4 and HK = 7, find KG and KF

The figure below is a parallelogram.

Find the value of x.

2x-1

A

D

AD=26

The figure below is a parallelogram. Find the values of x and y.

2x+3

4x-94y

6y-16

Theorem

If one pair of opposite sides of a quadrilateral is BOTH congruent and parallel, then the quadrilateral is a parallelogram.

EXAMPLES: Is there enough information to determine that the quadrilateral is a parallelogram? Explain. a.) b.)

x

x

Graph the parallelogram. Reflect it over the x –axis.

A(1,4), B(3,5) , C(6,1), D(4,0)

Theorem:

If 3 or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on EVERY transversal.